BRITISH ISLES FOR THE EPOCH JANUARY 1, 1915. 
25 
lines would be linear in the differences of latitude and longitude from a mean point 
within the region. 
Thus the magnetic potential Q is adequately expressed by 
where X and I are the differences of latitude and longitude from the mean point 
Xo and 4 as origin. 
Whence 
N = -^ = -A-aX-bl, 
ax 
cos (Xg + X) W = ^ = B + 6x + c/, 
cl 
so that 
aN a cos (Xg+x) w _ 
JF ax 
is a necessary condition. 
Causes within the region may be either electric currents or magnetic poles. The 
known electric currents in the earth and the air are too small to produce any 
magnetic effects that can be measured by survey apparatus and may therefore be 
ignored. There remains the possibility of unknown electric currents that may not 
give a magnetic potential, and of local magnetic poles which would contribute terms 
to the magnetic potential. These latter, being effectively singularities within the 
region, produce effects on the isomagnetic lines that are not adequately represented 
by linear formulae. Only by very numerous and properly selected stations could we 
expect to disentangle the terrestrial isomagnetic lines due to distant causes, which 
produce a potential and linear isomagnetics, from the true isomagnetics in which 
possible electric currents and local magnetic poles have an appreciable effect. 
The number of stations is, however, limited, so that if we determine (as we may) 
the best linear isomagnetics that are given by the data, we get only an approximation 
to the terrestrial lines, while the differences between the observed and the computed 
values of the element give an approximation to the disturbances in the region. No 
other course is open, but the results suggest where more detailed survey is required 
to improve the approximation. 
We may proceed then by determining the best linear isomagnetics (Force, 
Declination and Dip) or (North, West and Vertical components offeree) which fit the 
observations. The three components are analysed independently and we may then 
test whether they satisfy the condition for a potential. In general they do not; and 
the differences are usually so great that no known electric currents will account 
for them. The obvious explanation lies to hand that we have local attraction, not 
adequately represented by a magnetic potential giving linear contributions to the 
VOL. uoxix.— A. E 
